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The Golden Ratio is an irrational number. The first few digits look like this:
1.61803398874989484820... (and more ...)
solving x^2 = x + 1 gives φ
Phi has some rather starling properties
It appears that the way the human brain neuron pathways interoperate images uses the Golden Ratio to help decipher our surrounds
Some even go as far to say that it can determine a sense of perfection in what we see and also to determine if what we see is beautiful.
The influence in Nature is very prominent in DNA, cells, plants and even human faces all the way up to spiral Galaxies.
Many great buildings have taken into account this number.
Parthenon
The Fibonacci sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on forever. Each number is the sum of the two numbers that precede it. It's a simple pattern, but it appears to be a kind of built-in numbering system to the cosmos.
Leonardo Fibonacci came up with the sequence when calculating the ideal expansion pairs of rabbits over the course of one year. Today, its emergent patterns and ratios (phi = 1.61803...) can be seen from the microscale to the macroscale, and right through to biological systems and inanimate objects. While the Golden Ratio doesn't account for every structure or pattern in the universe, it's certainly a major player.
Fibonacci Spiral (Spiral of Archimedes)
Snail Shell
Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen from the side, and even the eye and ear itself (which follows along a spiral).
It's worth noting that every person's body is different, but that averages across populations tend towards phi. It has also been said that the more closely our proportions adhere to phi, the more "attractive" those traits are perceived. As an example, the most "beautiful" smiles are those in which central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than canines, and so on. It's quite possible that, from an evo-psych perspective, that we are primed to like physical forms that adhere to the golden ratio — a potential indicator of reproductive fitness and health.
1. Flower petals
The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five (pictured at left), the chicory's 21, the daisy's 34, and so on. Phi appears in petals on account of the ideal packing arrangement as selected by Darwinian processes; each petal is placed at 0.618034 per turn (out of a 360° circle) allowing for the best possible exposure to sunlight and other factors.
2. Seed heads
The head of a flower is also subject to Fibonaccian processes. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns.
Not surprisingly, spiral galaxies also follow the familiar Fibonacci pattern. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees. As an interesting aside, spiral galaxies appear to defy Newtonian physics. As early as 1925, astronomers realized that, since the angular speed of rotation of the galactic disk varies with distance from the center, the radial arms should become curved as galaxies rotate. Subsequently, after a few rotations, spiral arms should start to wind around a galaxy. But they don't — hence the so-called winding problem. The stars on the outside, it would seem, move at a velocity higher than expected — a unique trait of the cosmos that helps preserve its shape.
Philosophy! dis-information conspiracy?
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The Golden Ratio (why it is so irrational)
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